scholarly journals From the Lifshitz tail to the quenched survival asymptotics in the trapping problem

2009 ◽  
Vol 14 (0) ◽  
pp. 435-446 ◽  
Author(s):  
Ryoki Fukushima
Keyword(s):  
Trapping Problem ◽  
Lifshitz Tail

scholarly journals Supersymmetric Cluster Expansions and Applications to Random Schrödinger Operators

2021 ◽  
Vol 24 (1) ◽  
Author(s):  
Luca Fresta
Keyword(s):  
Density Of States ◽  
Local Density ◽  
Schrödinger Operators ◽  
Random Schrödinger Operators ◽  
Schrodinger Operators ◽  
Local Density Of States ◽  
Weak Disorder ◽  
Cluster Expansions ◽  
Strong Disorder ◽  
Lifshitz Tail

AbstractWe study discrete random Schrödinger operators via the supersymmetric formalism. We develop a cluster expansion that converges at both strong and weak disorder. We prove the exponential decay of the disorder-averaged Green’s function and the smoothness of the local density of states either at weak disorder and at energies in proximity of the unperturbed spectrum or at strong disorder and at any energy. As an application, we establish Lifshitz-tail-type estimates for the local density of states and thus localization at weak disorder.

Deterministic and probabilistic occupancy detection with a novel heuristic optimization and Back-Propagation (BP) based algorithm

2021 ◽  
pp. 1-13
Author(s):  
Nuzhat Fatema ◽  
Saeid Gholami Farkoush ◽  
Mashhood Hasan ◽  
H Malik
Keyword(s):  
Convergence Rate ◽  
Search Algorithm ◽  
Gravitational Search Algorithm ◽  
Hybrid Approach ◽  
Experimental Studies ◽  
Back Propagation ◽  
Heuristic Optimization ◽  
Local Minima ◽  
Occupancy Detection ◽  
Trapping Problem

In this paper, a novel hybrid approach for deterministic and probabilistic occupancy detection is proposed with a novel heuristic optimization and Back-Propagation (BP) based algorithms. Generally, PB based neural network (BPNN) suffers with the optimal value of weight, bias, trapping problem in local minima and sluggish convergence rate. In this paper, the GSA (Gravitational Search Algorithm) is implemented as a new training technique for BPNN is order to enhance the performance of the BPNN algorithm by decreasing the problem of trapping in local minima, enhance the convergence rate and optimize the weight and bias value to reduce the overall error. The experimental results of BPNN with and without GSA are demonstrated and presented for fair comparison and adoptability. The demonstrated results show that BPNNGSA has outperformance for training and testing phase in form of enhancement of processing speed, convergence rate and avoiding the trapping problem of standard BPNN. The whole study is analyzed and demonstrated by using R language open access platform. The proposed approach is validated with different hidden-layer neurons for both experimental studies based on BPNN and BPNNGSA.

Bayesian estimation of ordinary differential equation models when the likelihood has multiple local modes

2018 ◽  
Vol 24 (2) ◽  
pp. 117-127
Author(s):  
Baisen Liu ◽  
Liangliang Wang ◽  
Jiguo Cao
Keyword(s):  
Likelihood Function ◽  
Local Modes ◽  
Predator Prey ◽  
Complex Dynamic Systems ◽  
Ode Models ◽  
Differential Equation Models ◽  
Model Complex ◽  
Noisy Measurements ◽  
Optimizing Algorithm ◽  
Trapping Problem

Abstract Ordinary differential equations (ODEs) are popularly used to model complex dynamic systems by scientists; however, the parameters in ODE models are often unknown and have to be inferred from noisy measurements of the dynamic system. One conventional method is to maximize the likelihood function, but the likelihood function often has many local modes due to the complexity of ODEs, which makes the optimizing algorithm be vulnerable to trap in local modes. In this paper, we solve the global optimization issue of ODE parameters with the help of the Stochastic Approximation Monte Carlo (SAMC) algorithm which is shown to be self-adjusted and escape efficiently from the “local-trapping” problem. Our simulation studies indicate that the SAMC method is a powerful tool to estimate ODE parameters globally. The efficiency of SAMC method is demonstrated by estimating a predator-prey ODEs model from real experimental data.

scholarly journals Air trapping problem during infiltration on the large areas

2018 ◽  
Vol 44 ◽  
pp. 00178
Author(s):  
Witold Tisler ◽  
Adam Szymkiewicz
Keyword(s):  
Water Flow ◽  
Richards Equation ◽  
Shallow Water Table ◽  
Two Phase ◽  
Infiltration Process ◽  
Soil Skeleton ◽  
Irrigation Effect ◽  
Volume Method ◽  
The Impact ◽  
Trapping Problem

The process of flow modeling in unsaturated porous medium is often found in many fields of sciences: geology, fluid mechanics, thermodynamics, microbiology or chemistry. Problem is relatively complicated due to complexity of the system which contains three phases: water, air and soil skeleton. The flow of water in such a medium can be described using two-phase (2PH) flow formulation, which accounts the inflow of air and water phases, or with simplified model known as Richards (RE) equation where only water flow is taken into account. In many well known programs available in the market (like SeepW, STOMP) the primary interest is only the water flow and the flow of air is omitted. As a result Richard equation in used more often. It’s main assumption is that pore air is continuous and has connection with atmospheric air which is equivalent to infinite mobility of the air phase during all simulation. This paper presents a brief review of the influence of the air phase in soil on water flow and pore pressure generation, with focus on applications related to infiltration process occurring in the large areas. An irrigation effect of rice fields with shallow water table has been investigated. To assess the impact of the gas phase various lengths of the infiltration zone have been considered. Numerical simulations are carried out to investigate the differences between the Richards equation and the two-phase flow model, using an in-house code based on the finite volume method.

The fate of the Lifshitz tail for condensed bosons

1992 ◽  
Vol 4 (7) ◽  
pp. 1729-1742 ◽  
Author(s):  
D K K Lee ◽  
J M F Gunn
Keyword(s):  
Lifshitz Tail
Sign in / Sign up

Export Citation Format

Share Document